Neutral Sigma Baryon

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Weighing in at 1192 MeV, the middle-weight $\Sigma$ baryon is also the the electrically neutral one.

The $\Sigma$ Baryons are a trio of strange, slightly heavy cousins to everyday particles like the proton and the neutron. We’ve already talked at length about the charged $\Sigma$ baryons. Today, we’re focusing on their electrically neutral sibling, $\Sigma^{0}$.

While the decay resistant charged $\Sigma$ baryons - with their unusually long lifetimes - certainly qualify as “strange” particles, the $\Sigma^{0}$ feels far less strange. At least at first.

The $\Sigma^{0}$ decays rapidly. Tens of trillions of times faster than its charged siblings $\Sigma^{+}$ or $\Sigma^{-}$. If you’re into really small numbers, or just to measure time in seconds, that’s a decimal point followed by 19 zeroes before you get 7 and then a four.

$$ 0.000000000000000000074\,\mathrm{seconds}$$

That’s too short a time for us to fathom, but its about right for an unstable particle that heavy.

Remember, it is STRANGE that the typical lifetime for strange baryons like $\Lambda^{0}$ or the Charged $\Sigma$’s can be measured in nanoseconds.

So why does the $\Sigma^{0}$ baryon decay so quickly? OR why do we even consider it to be in the “Strange” family?

Decays

One reason to consider $\Sigma^{0}$ “strange” is because it decays to a strange particle. Specifically, it decays, 100 percent of the time, to a $\Lambda^{0}$:

$$ \Sigma^{0} \rightarrow \Lambda^{0} + \gamma$$

In the process, the $\Sigma^{0}$ throws out a photon - that is, a $\gamma$ ray - which itself might be hard to explain. You see, photons carry the electromagnetic force. Photons are passed around like baseballs between particles that have an electric charge. Photons can be thought of as building blocks for electric and magnetic fields. SO what business does the uncharged $\Sigma^{0}$ - or $\Lambda^{0}$ for that matter - have interacting with a photon?

Electrically neutral pions, you might recall, decayed into a PAIR of photons. So perhaps it’s not weird. But $\pi^{0}$ decays were something of an anomaly. Literally. You might recall that $\pi^{0}$ decayed to two photons,

$$\pi^{0}\rightarrow \gamma + \gamma$$

because of the chiral anomaly. It involved these wild, quantum mechanical beasts known as instantons. Very nonlinear, very intricate, unusual stuff. In some sense, the neutral pion just vaporized into the electromagnetic field.

This is decidedly NOT what happens with $\Sigma^{0}$. It doesn’t vaporize. It just decays like any other particle. So what gives?

To understand how an electrically neutral particle could spit out a photon, we have to look inside the baryon to that subnuclear goo of quarks and gluons.

Baryon Innards

The $\Sigma$ baryons are all bona fide strange particles, they all have a strange quark. $\Sigma^{+}$ had two up quarks and a strange quark. $\Sigma^{-}$ shad two down quarks and a strange quark.

Can you guess what a $\Sigma^{0}$ has?

One of each. Up, down and strange.

But wait. Wasn’t the $\Lambda^{0}$ also made up from an up quark, a down quark and a strange quark? Well yes. And that fact explains in fact, why the $\Sigma^{0}$ decays so quickly. It decays to the $\Lambda^{0}$ because they both share the same number and kind of internal or valance quarks.

As it turns out, the $\Sigma^{0}$ is something of an “Excited” version of the $\Lambda^{0}$. Internally, you might say that the up and down quarks are buzzing around in a slightly different configuration. A configuration with slightly more energy. They’re a little more spun up, as it were. That bit of spin energy gets released by the emission of a photon, leaving that bag of quarks and gluons with lower internal energy, otherwise known as the particle $\Lambda^{0}$.

$E = mc^{2}$ after all just means that the mass is proportional to energy.

Including Photons

The internal structure of the $\Sigma^{0}$ also explains why an electrically neutral particle can throw out a photon. It’s just electrically neutral on average. The average value of the electric charges of all the quarks is zero. But individually, they each have a charge.

This brings us back to the story of the neutron. While the average electric charge of a neutral baryon is zero, the electromagnetic field need not be identically zero.

Like the neutron or the earth, the $\Sigma^{0}$ baryon has a nonzero magnetic dipole moment. It probably should also has an electric dipole moment. All this means is that the electromagnetic fields kind of averages out to zero, but are still smeared out, in a way.

And it’s these smeared out configurations that allow the $\Sigma^{0}$ to throw out a photon and decay to a $\Lambda^{0}$. Or at least, that’s another fun way to think about it.

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